A rod with circular cross-section area $2 \mathrm{~cm}^{2}$ and length $40 \mathrm{~cm}$ is wound uniformly with 400 turns of an insulated wire. If a current of $0.4 \mathrm{~A}$ flows in the wire windings, the total magnetic flux produced inside windings is $4 \pi \times 10^{-6} \mathrm{~Wb}$. The relative permeability of the rod is
(Given : Permeability of vacuum $\mu_{0}=4 \pi \times 10^{-7} \mathrm{NA}^{-2}$)
Solution
Magnetic field in the Solenoid,
<br/><br/>$$
\begin{aligned}
& \mathrm{B}=\mu_0 \mu_r \mathrm{nI} \\\\
& \text { Magnetic flux, } \phi=\mathrm{N}(\mathrm{BA}) \\\\
& \phi=N\left(\mu_0 \mu_r n I A\right) \\\\
& \Rightarrow 4 \pi \times 10^{-6}=400\left(4 \pi \times 10^{-7} \mu_r \times \frac{400}{0.4} \times 0.4 \times 2 \times 10^{-4}\right) \\\\
& \Rightarrow \frac{1}{40}=\mu_r \times 8 \times 10^{-2} \\\\
& \Rightarrow \mu_r=\frac{100}{320}=\frac{5}{16}
\end{aligned}
$$
About this question
Subject: Physics · Chapter: Magnetic Effects of Current · Topic: Biot-Savart Law
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